feedback system

my question is how making the vehicle to get into almost desired speed equation is u=ke.
e=r-y
r -reference speed
y-output feed back to input
k-time instant
if on speed of vehicle is 30 km/hr.my reference speed is 70 km/hr.
for the first time we get e=40 as feedback.and further this 40 is carried out in what way in order to get the vehicle to 70 km/hr speed.please help me.thank you in advance

Having a controller in the loop, an error of 40 means the controller will attempt to change the controlled variable(speed) using the parameters under its control (e.g. Increasing fuel flow, depressing the accelerator, etc.) in order to bring the error to 0.

in my above post u=ke
u control signal
e error
k scaling or mapping factor. It is used as a "weight" or "gain"

from this can u explain what is k mean.all this stuff are related of controlling speed of car

what is k?i mean what is scaling factor or mapping vector or what is gain in such system

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As Georacer noted, this is a proportional controller. As you noted the control signal is simply the error times k, meaning the output is proportional to the error. In this particular case the controller is just a gain of k.

Take k=50 for your previous example. e = 40 so u= 50*40= 2000. Assuming it takes time for the car to speed up, the next time we sample the error, the vehicle's speed has come to 40km/hr, so, as before, e=70 - 40 = 30 and u=30*50 = 1500.

This process continues to converge to 0 until e becomes negative, at which point, the car has exceeded the commanded speed. If the gain if the controller, k, is too high, the vehicle's speed will continue to oscillate about the set point.

As k increases, the error decreases. It is like an open loop in operational amplifiers. When you insert a feedback the gain tend to be constant at higher frequencies. Your system tend to be faster than with a lower k. It is normally true on first order systems.
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